Why can I not put an edge loop around this model?
I don't know why it happens but I know how to resolve:
Every part of the mesh where there are 2 faces loops between two spokes, delete the 4 vertices inbetween (they also are not selectable as edge loop), then recreate them, extruding or bridging edge loops and then loop cutting and grabbing in the right position.

Edit: deleting and recreating just one vertex is enough.